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# Class 8 RD Sharma Solutions – Chapter 14 Compound Interest – Exercise 14.2 | Set 2

• Last Updated : 08 Apr, 2021

### Question 11. Rakesh lent out Rs. 10000 for 2 years at 20% per annum, compounded annually. How much more he could earn if the interest be compounded half-yearly?

Solution:

We have,

Principal (p) = Rs 10000

Rate (r) = 20% per annum

Time (t) = 2years

By using the formula,

A = P (1 + R/100)n

= 10000 (1 + 20/100)2

= 10000 (120/100)2 = Rs 14400

When the interest is compounded half-yearly

New values are

Rate of interest becomes= 20/2% = 10%

Time = 2Ã—2 years = 4years

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 10000 (1 + 10/100)4

= 10000 (110/100)4 = Rs 14641

âˆ´ Rakesh could earn Rs (14641 â€“ 14400) = Rs 241 more

### Question 12. Romesh borrowed a sum of Rs. 245760 at 12.5% per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.

Solution:

Given:

Principal (p) = Rs 245760

Rate (r) = 12.5% per annum

Time (t) = 2years

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 245760 (1 + 12.5/100)2

= 245760 (112.5/100)2

= Rs 311040

Now, When compounded semi-annually,

Rate = 12.5/2% = 6.25%

Time = 2Ã—2 years = 4years

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 245760 (1 + 6.25/100)4

= 245760 (106.25/100)4 = Rs 313203.75

âˆ´ Romesh gain is Rs (313203.75 â€“ 311040) = Rs 2163.75

### Question 13. Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12 Â½ % per annum, the interest being compounded half-yearly.

Solution:

Given,

Principal (p) = Rs 8192

Rate (r) = 12 Â½ % per annum = 25/2Ã—2 = 25/4% = 12.5/2% (half-yearly)

Time (t) = 18 months = 18/12 = 1 Â½ years = (3/2) Ã— 2 = 3years

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 8192 (1 + 12.5/2Ã—100)3

= 8192 (212.5/200)3

= Rs 9826

âˆ´ Amount is Rs 9826

### Question 14. Find the compound interest on Rs. 15625 for 9 months, at 16% per annum, compounded quarterly.

Solution:

Given,

Principal (p) = Rs 15625

Rate (r) = 16% per annum = 16/4 = 4% (quarterly)

Time (t) = 9 months = 9/12 Ã— 4 = 3quarters of a year

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 15625 (1 + 4/100)3

= 15625 (104/100)3

= Rs 17576

âˆ´ CI = Rs 17576 â€“ 15625 = Rs 1951

### Question 15. Rekha deposited Rs. 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded quarterly, find the interest received by Rekha after one year

Solution:

Given is,

Principal (p) = Rs 16000

Rate (r) = 20% per annum = 20/4 = 5% (quarterly)

Time (t) = 1 year = 4 quarters of a year

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 16000 (1 + 5/100)4

= 16000 (105/100)4= Rs 19448.1

âˆ´ CI = Rs 19448.1 â€“ 16000 = Rs 3448.1

### Question 16. Find the amount of Rs. 12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.

Solution:

We have the following set of values,

Principal (p) = Rs 12500

Rate1 (r) = 15% and Rate2 = 16%

Time (t) = 2 years

By using the formula,

A = P (1 + R1/100 Ã— 1 + R2/100) = 12500

Substituting the values we have,

(1 + 15/100 Ã— 1 + 16/100) = 12500 (1.15 Ã— 1.16)

= Rs 16675

âˆ´ Amount after two years is Rs 16675

### Question 17. Ramu borrowed Rs. 15625 from a finance company to buy scooter. If the rate of interest be 16% per annum compounded annually, what payment will he have to make after 2 Â¼ years?

Solution:

Given details are,

Principal (p) = Rs 15625

Rate (r) = 16%

Time (t) = 2 Â¼ years

By using the formula,

A = P (1 + R/100 Ã— 1 + R/100)= 15625

Substituting the values we have,

(1 + 16/100)2 Ã— (1 + (16/4)/100)= 15625

(1 + 16/100)2 Ã— (1 + 4/100)= 15625

(1.16)2 Ã— (1.04)= Rs 21866

âˆ´ Amount after 2 Â¼ years is Rs 21866

### Question 18. What will Rs. 125000 amount to at the rate of 6%, if the interest is calculated after every four months?

Solution:

Given,

Principal (p) = Rs 125000

Rate (r) = 6% per annum

Time (t) = 1 year

Since interest is compounded after 4months, interest will be counted as 6/3 = 2% and,

Time will be 12/4 = 3quarters

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 125000 (1 + 2/100)3

= 125000 (102/100)3

= Rs 132651

âˆ´ Amount is Rs 132651

### Question 19. Find the compound interest at the rate of 5% for three years on that principal which in three years at the rate of 5% per annum gives Rs. 12000 as simple interest.

Solution:

Given,

Simple interest (SI) = Rs 12000

Rate (r) = 5% per annum

Time (t) = 3 years

SI = (PTR)/100P

= (SIÃ—100)/(TÃ—R)

Solving the equations,

= (12000Ã—100) / (3Ã—5)

= 1200000/15= 80000

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 80000 (1 + 5/100)3

= 80000 (105/100)3

= Rs 92610

âˆ´ CI = Rs 92610 â€“ 80000 = Rs 12610

### Question 20. A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs. 482 more. Find the sum.

Solution:

We have,

Rate (r) = 20% per annum = 20/2 = 10% (half yearly)

Time (t) = 2 years = 2 Ã— 2 = 4 half years

Principal be = Rs P

P (1 + R/100)n â€“ P (1 + R/100)n

= 482P (1 + 10/100)4 â€“ P (1 + 20/100)2

= 482P (110/100)4 â€“ P (120/100)2

= 482P (1.4641) â€“ P (1.44)

= 4820.0241P

= 482P = 482/0.0241

= 20000

âˆ´ Amount is Rs 20000

### Question 21. Simple interest on a sum of money for 2 years at 6 Â½ % per annum is Rs. 5200. What will be the compound interest on the sum at the same rate for the same period?

Solution:

Given is,

Rate = 6 Â½ % per annum = 13/2%

Simple Interest (SI) = Rs 5200

Time (t) = 2 years

By using the formula,

SI = (PTR)/100P = (SIÃ—100) / (TÃ—R)

= (5200Ã—100) / (2Ã—13/2)

= (5200Ã—100Ã—2) / (2Ã—13)

= 1040000/26

= Rs 40000

Now, P = Rs 40000R

= 13/2% = 6.5%T = 2years

By using the formula,

A = P (1 + R/100)n

Substituting the values we have,

= 40000 (1 + 6.5/100)2

= 40000 (106.5/100)2

= Rs 45369

âˆ´ CI = Rs 45369 â€“ 40000 = Rs 5369

### Question 22. What will be the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at the rate of 5% per annum gives Rs. 1200 as simple interest.

Solution:

Rate = 5 % per annum

Simple Interest (SI) = Rs 1200

Time (t) = 3 years

By using the formula,

SI = (PTR)/100P = (SIÃ—100) / (TÃ—R)

= (1200Ã—100) / (3Ã—5)

= 120000/15

= Rs 8000

Now, P = Rs 8000R

= 5%T = 3years

By using the formula,

A = P (1 + R/100)n

= 8000 (1 + 5/100)3

= 8000 (105/100)3

= Rs 9261

âˆ´ CI = Rs 9261 â€“ 8000 = Rs 1261

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